What are the four essential elements of a number in floating-point notation?

Answer 1

The four essential elements of a number in floating-point notation are the sign bit, exponent, mantissa (or significand), and base. The sign bit determines whether the number is positive or negative. The exponent represents the power to which the base is raised. The mantissa holds the significant digits of the number. The base is typically 2 for binary floating-point numbers.

Answer 2

A

numberexpressed as a mantissa value qualified by an exponent value, e.g. (0.123 456,-4) to mean 0.123 456 × 10

-4else 0.123 456 × 16

-4, etc., depending on the implied radix, i.e. numbers in which the true value is obtained by floating the decimal (or equivalent) point the indicated number of places, four to the left in the above example, producing 0.000 0123 456 if with a decimal radix. With

normalizationof the mantissas to an appropriate set range (typically to the highest

arithmeticvalue less than 1, as illustrated here), this notation allows retention, within a fixed amount of space, of comparable numeric significance over a wide range of numeric size. In external display, it is usual to adopt decimal radix and the convention of using E preceding the exponent, e.g. 0.987 6 E + 12 to mean 0.987 6 × 10

12.

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